What is an incomplete sentence which missing a subject called?

An incomplete sentence that is missing a subject is called a phrase.

Here's why:

* Sentence: A complete thought that has a subject and a verb.

* Phrase: A group of words that lacks a subject and verb, and therefore cannot stand alone as a complete sentence.

Example:

* Incomplete Sentence (Phrase): "Running through the park."

* This is missing a subject (who is running?).

* Complete Sentence: "The dog is running through the park."

* This includes both a subject (dog) and a verb (is running).